President, Gravity Research Institute, Shantiniketan1, 983 David Walker Drive, Tavares, FL, United States

In our previous articles, we explained various issues by using our probabilistic gravity such as constants of Nature including strong coupling, information, consciousness, entanglement, cause of Alzheimer’s, spooky dark matter, multiplicity of particles, Brownian motion, synchronicity and some issues in biology etc. etc. Here, we extend it to medical and engineering issues, while addressing the Clay mathematics institute’s problem about Navier-Stokes Equation on their web site.

Alzheimers; Entanglement; Biology

Navier-Stokes Equation is a partial differential equation for a fluid flow. Its medical and engineering significance is adequately described in [1-3], demonstrating the importance of its solution. “Turbulent flows by coughs and sneezes...have come to the forefront because of COVID 19” [2]. However, its solution is impossible. Nevertheless, the Clay Institute has sponsored a prize for its solution as below. Its website breaks it down into four problems. The prize requires one to solve any one of them. In all four, the fluid is assumed incompressible. “They are:

- Existence and smoothness in solutions in three dimensions. Here the fluid is assumed to fill the whole of infinite space. Given any initial smooth velocity field, prove that a smooth solution to the equation exists for all positive times, coinciding with the specified initial field.
- Existence and smoothness of solutions in the three-dimensional flat torus. The same question, but now assuming that space in flat torus-a rectangular box with opposite faces identified. This version avoids potential problems caused by the infinite domain assumed in the first version, which does not match reality and might cause bad behavior for silly reasons.
- Breakdown of solutions in three dimensions. Prove that (1) is wrong. That is find an initial field for which a smooth solution does not exist for all positive times, and prove that statement.
- Breakdown of solutions in the three dimensions flat torus. Prove that (2) is wrong. [1]”

We test our quantum gravity for the solution of the above, we touch base about the fundamental cause of meditation and other tidbits.

Our probabilistic theory [4,5], first put on the preprint achieve, implies in short that the probability of an interaction between any two particles is inversely proportional to their separation in Planck lengths i.e. one particle interacts with multiple particles, each one generating a tiny black hole, though too tiny to be noticeable to us as black holes, they can disturb the fluid flow. Each entangled particle has its own gravitational effect per [6] now backed by Feynman’s 1957 view, dug out by Tim Folger of Scientific American [7]. Each Planck time has its own significance, because the natural log of the age of the universe in Planck times (10E60 Planck times) comes out admirably close to Feynman’s mystical number 137 [8] within a decimal point. After numerous presentations, we placed it on a future grave yard stone.

Dr. Stewart’s statement says, “….particles interact with each other [1] p 234”, “This very statement gives birth to a black hole: When two nucleons interact with each other, they create a black hole per Karl Schwarzschild’s impressive equation as in equation 1 of [9]. This creates a strong coupling with a known force of 10E40g which diminishes to gravity, outside an atom [9]. Existence of gravity indicates the preexistence of black holes that create gravity waves. The implicit synonymy of strong coupling and gravitation is elaborated in [10] and [11] with [11] taking a relativistic approach. Such black holes and their forces appear ON and OFF per our probabilistic (statistical) gravity [8], implying they are not continuous. The Navier-Stokes equation is based on the Newtonian law of gravity equating force to the product of mass and acceleration, which have continuity, questioning its validity at Planck scale. The self-supporting consequence of discontinuity is that it provides for the information, as claimed in [8]. Radiation of information in [3] is an alternate description of the same idea. Somehow once we made now Nobel Laureate Kip Thorne smile in GR17 Conference in Dublin, Ireland mentioning our proposal of the synonymy of nuclear force and gravitation.

The subject problem about the Navier-Stokes equation asks whether singularities can occur in initial value problems, for a fluid occupying either the whole of space or a flat torus. [1] p 225. If a singularity occurs in a finite time, the result is likely to be blown up, unless the singularity somehow unravels itself subsequently, which seems unlikely, [1] p 225. Dr. Stewart mentions on p 221, “Many different scenarios that might lead to singularities have been investigated.” A black hole leads to singularity per accepted physics. Our quantum gravity has innumerable black holes therefore, singularities are their undeniable consequences at all Planck times i.e. in all initial value problems. Therefore, (1) and (2) are wrong, and (3) and (4) are right. It is that simple! Dirac craved for simplicity. “Analytical solutions aren’t possible in the Navier-Stokes equation for turbulent flows [1]” Obviously so, the analytical solutions are devoid of innumerable and invisible tiny black holes that disturb the smoothness of the flow. There are additional substantiations.

We agree with Charles Fefferman about Navier-Stokes equation. “In his article about this problem on the Clay institute website [http://www.claymath.org/millennium/Navier-Stokes_Equations/], Charles Fefferman writes: Standard methods (from partial differential equations) appear inadequate to settle the problem. Instead, we probably need some deep, new idea. [1] p 227” The deepness of our idea is in the following published on the subject of "Reflections" in [12] editted by Shantiniketan's resident, psychiatric and medical Dr. Kedar Berma. “Soon after learning the Newton’s Law of Gravity in the high school, I asked the teacher in my childish language then, about its failure to explain the strong binding energy at the smallest particles. The teacher highly appreciated the question and replied that Einstein may have explained it. Einstein did so in 1919, but his explanation was non-quantum and was not accepted. Quantum mechanics was not developed then to explain it anyway. So in 3/1999, we found a partial quantum mechanical solution, now in our book [5] and used it to ask a question to Nobel Laureate, Dr. Weinberg as detailed in [6]. Our references in [6] imply the reflections of that question, one addressing the problem of dark matter, now at the forefront of physics as explained in (DOI: 10.17265/2159-5348/2015.05.008) [9] matching the case of Lord Shiva’s Tandam Natyam.” We were proud to see Lord Shiva’s dance picture in The Wall Street Journal on 4/5/2016 with a figure head: CERN’s Shiva, which we referred in [13]. In the words of the late scientist Carl Sagan on that dance, “It is the clearest image of the activity of God which any art or religion can boast of [14].”

The above childish question to the teacher was to verify the lower boundary condition of the inverse square law. Later we learnt that his doubt in his own inverse square formula made Newton delay its publication for over a decade until forced by the Royal Society. We deserve his blessings from Heaven.

Referring Occam’s razor and [15] for author’s explicit view, “Particles have a quantum mouth, and a body they can stretch, and get entangled” says Dr. Zacharia P. Thundy, author of dozens of such books, who has devoted two pages with a comment: “The simplest solution needs to be the right one [16]” A nucleon can stretch out of the divisible atom and interact with other nucleons, causing a strong coupling.

Our 2020 horizon [17] hypotheses the multiplicity of soul in the Higgs field. One possibility of such a field is speculated by Dr. Weinberg in [18]. Surprisingly, Bhagwat Gita 13.1-7 repeatedly asserts such a field. We see the possibility of the fundamental cause of meditation in the multiplicity of soul (mind) in the HIGGS field in [17].

Talking about four cases of fluid flows with their pictures in a figure (Figure 43) [1] p 227, it states “The complexity of the flow in images like Figure 43 drives home the difficulties that are likely to be encountered when seeking these ideas. Undaunted, mathematicians are soldering on, seeking simple principles within the apparent complexities [1] p 227” The subject Figure 43 (with a figure head: Zooms into a turbulent flow, ….) in the book [1], and also the one colorfully shown in [2] look more like a quantum foam depicted by Stephen Hawking in his book rather than one showing a smooth flow, as if it is affected by the quantum effects in the fluid, substantiating our application of quantum gravity and questioning the smoothness of the flow. It would be interesting to see similar pictures of Bermuda Triangle accidents with no known cause.

“There is a physical problem that is common to many fields, that is very old, and that has not been solved. It is not the problem of finding new fundamental particles, but something left over from a long time ago---over a hundred years. Nobody in physics has really been able to analyze it mathematically satisfactorily in spite of its importance to the sister sciences. It is the analysis of circulating or turbulent fluids [2,19]”. The sister sciences include medical science about blood flow through veins and aeronautical engineering. Dr. Perry adds in the first paragraph, “Evan today in the age of supercomputers, the need for understanding, modeling, and predicting aspects of turbulent flows has, if anything, increased. Reliably simulating turbulent flows still requires more theoretical advances, and Feynman’s vision of “Solving the problem of turbulence” remains elusive [2]” The theoretical advance we propose is our quantum theory of gravity devoid of the need of unfound gravitons.

Einstein’s 1919 paper [20] concludes synonymy of nuclear force and gravity without needing the graviton. He transcended particle mechanisms anyway. In 1905, when Einstein investigated Brownian motion, there was no quantum mechanics. Considering Brownian motion as a non-zero turbulence, we need to find its fundamental quantum mechanical cause, because that is the one that gets pronounced with higher fluid velocities. Our quantum gravity [8], goes deeper into explaining the Brownian motion. Unlike cosmic black holes which are not surrounded by fluid, turbulence must be increased with high velocity fluid flow and black hole combinations, affecting the smoothness of the blood flow.

A preoccupation with the notion that a particle cannot interact with more than one particle simultaneously denies one to explain the proven observation of multiplicity of particles. What is obligatory and therefore of primary importance in string theory is the quantum theory of gravity combined with Feynman's mystical number ALPHA. God made Nature somehow equates the cumulative effect of the sum of all coupling constant forces to the force of gravity we perceive, questioning the need for an unfound graviton missing for a century. Gravitons cannot create information needed for the consciousness that exists in life, bypassing biology/medical science from the theory of everything. The wonderful author of the book, “GOD EQUATION” says “WANTED: THE GRAVITON [3]”. There already is a God Particle (Higgs Boson) in the Higgs Field derived from its own equation. String theory may someday prove the roundness of the earth, but if gravity is the cumulative effect of the coupling constants of Nature as implied by our quantum theory of gravity, graviton will never be found even if we spend another century to find it. The standard model has no graviton for a reason. String theory is a word by Ed Witten, the word is not written (accepted). The need for the graviton is based on the assumption that gravity is a fundamental interaction. Such assumption implies that Nature created the coupling constants for nothing. Nature creates nothing useless per Nobel Laureate Dr. Tagore; we agree. The string theory assumes permanent unverifiable dimensions. The probabilistic string like connections between elementary particles, implicit in our theory, are observed in quantum tunneling as sketched in [5,21].

The reason why the Navier-Stokes equation cannot have a solution is that its derivation uses classical (Newtonian) continuum gravity which we say is affected on the cumulative effect of the manifestation of the forces of black holes generated by particle interactions which are fundamentally non-continuous point like sources at Planck scales per our quantum theory of gravity. In other words, the fluid flows are affected by our promising quantum theory of gravity which is devoid of gravitons. The new horizon implies that the quest for TOE in [3] is based on probabilistic mathematics; not deterministic one, assumed in [3]. Our probabilistic approach can substitute for the others not so successful.

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**Citation:** Goradia SG (2021) Quantum Effects Challenge Navier-Stokes Equation. J Alzheimers Neurodegener Dis 7: 053.

**Copyright:** © 2021 Shantilal Gangadas Goradia, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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